Time alue of Money

The basic concept of a net present value procedure is that a dollar in hand today is worth more than a dollar to be received sometime in the future. A dollar is worth more today than tomorrow because today’s dollar can be invested and can generate earnings. In addition, the uncertainty of receiving a dollar in the future and inflation make a future dollar less valuable than if it were received today.

The procedure for accounting for the delay in receiving funds or the income given up is to discount, or penalize, future cash flows. The longer you must wait to receive them, the more heavily you must discount them. This discounting procedure converts the cash flows that occur over a period of future years into a single current value so that alternative investments can be compared on the basis of that single value. This conversion of flows over time into a single figure via the discounting procedure takes into account the opportunity cost of having money tied up in the investment.

For example, assume that a manager can earn an 8% annual return on funds invested in his or her business. Based on this return, if the manager invests $681 today, then the investment will be worth $1,000 in five years (Table 1).

Year

Beginning

Interest

of Year

Rate

Amount at End of Year

Table 1. Time Value of Money

Value

Annual Interest

1

$681

x

8%

=

$54

$735

2

735

x

8%

=

59

794

3

794

x

8%

=

64

858

4

858

x

8%

=

69

926

5

926

x

8%

=

74

1,000

To adjust money for its future value, you use compounding (as in the example) to obtain the future value of a current sum. Every year, you add an amount to the money you already have based on the rate of return you earn. You do the reverse to calculate the present value of money you could receive in the future.

To calculate a present value—or discount future earnings to the present—assume, for example, that a manager earning 8% on his or her capital will receive $1,000 at the end of each

2

year for the next five years. The discount factor for money received at the end of the first year, assuming an 8% rate, is 0.9259. You can find the discount factor of 0.9259 in the appendix at the point where year one and 8% meet. Hence, the $1,000 received at the end of the first year has a present value of only $925.90 ($1,000 x 0.9259). In similar fashion, you can calculate the present value of the $1,000 received at the end of years two through five using the discount factors from the appendix for 8% and the appropriate years.

You can then determine the present value of this flow of money as the sum of the annual present values. So the present value of an annual flow of $1,000 for each of five years (assuming an 8% discount rate) is only $3,992.60. As a manager, you would be equally well off if you were to receive a current payment of $3,992.60 or the annual payment of $1,000 per year for five years, assuming an 8% discount rate. In essence, discounting reverses the compounding process and converts a future sum of money to a current sum by discounting or penalizing it for the fact that you don’t have it now, but have to wait to get it and consequently give up any earnings you could obtain if you had it today.

1

$1,000

x

0.9259

=

$925.90

2

1,000

x

0.8573

=

857.30

3

1,000

x

0.7938

=

793.80

4

1,000

x

0.7350

=

735.00

5

1,000

x

0.6806

=

680.60

Table 2. Computations to Discount to Present Value

Year

Using these concepts of the time value of money, you can determine the net present value (NPV) for a particular investment as the sum of the annual cash flows discounted for any delay in receiving them, minus the investment outlay.

Cash

Discount

Present

Flow

Factor

Value

Net Present alue

Total $3,992.60

In mathematical notation this set of computations can be summarized as: